How to combine three non-orthogonal cylinders with sphere
It might be an idea to use the skin modifier in combination with particles? It's pretty easy to set up and manipulate.


Create a mesh and then in Edit Mode delete 'Only Faces' - essentially leaving
you with a wire-frame.
Add the skin modifier and then a sub-surf modifier to smooth.
Create a Sphere object.
Add a particle system set to hair and choose Verts from Advanced
settings.
Under Display choose the Sphere object.


The particle system will have to be moved up to the top of the modifier stack.